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2012 Random walks with unbounded jumps among random conductances I: Uniform quenched CLT
Christophe Gallesco, Serguei Popov
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Electron. J. Probab. 17: 1-22 (2012). DOI: 10.1214/EJP.v17-1826

Abstract

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched uniform invariance principle for the random walk. This means that the rescaled trajectory of length n is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval of length $O(\sqrt{n})$ around the origin.

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Christophe Gallesco. Serguei Popov. "Random walks with unbounded jumps among random conductances I: Uniform quenched CLT." Electron. J. Probab. 17 1 - 22, 2012. https://doi.org/10.1214/EJP.v17-1826

Information

Accepted: 4 October 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60100
MathSciNet: MR2988400
Digital Object Identifier: 10.1214/EJP.v17-1826

Subjects:
Primary: 60J10
Secondary: 60K37

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Vol.17 • 2012
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